Density Waves Excited by Low-Mass Planets in Protoplanetary Disks II: High-Resolution Simulations of the Nonlinear Regime

We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using 2D local shearing box simulations with the grid-based code Athena at high spatial resolution (256 grid points per scale height h). The nonlinear evolution results in the wave steepening into a shock, causing damping and angular momentum transfer to the disk. On long timescales this leads to spatial redistribution of the disk density, causing migration feedback and potentially resulting in gap opening. Previous numerical studies concentrated on exploring these secondary phenomena as probes of the nonlinear wave evolution. Here we focus on exploring the evolution of the basic wave properties, such as its density profile evolution, shock formation, post-shock wave behavior, and provide comparison with analytical theory. The generation of potential vorticity at the shock is computed analytically and is subsequently verified by simulations and used to pinpoint the shock location. We confirm the theoretical relation between the shocking length and the planet mass (including the effect of the equation of state), and the post-shock decay of the angular momentum flux carried by the wave. The post-shock evolution of the wave profile is explored, and we quantitatively confirm its convergence to the theoretically expected N-wave shape. The accuracy of various numerical algorithms used to compute the nonlinear wave evolution is also investigated: we find that higher order spatial reconstruction and high resolution are crucial for capturing the shock formation correctly.Comment: single column, 31 pages, 8 figures, 1 table, ApJ in press, minor corrections mad

Langmuir wave linear evolution in inhomogeneous nonstationary anisotropic plasma

Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for the wave action density, and the conditions for the action conservation are formulated. In homogeneous plasma, the wave field E universally scales with the electron density N as E ~ N^{3/4}, whereas the wavevector evolution varies depending on the wave geometry

Separated spin-up and spin-down evolution of degenerated electrons in two dimensional systems: Dispersion of longitudinal collective excitations in plane and nanotube geometry

Applying the separated spin evolution quantum hydrodynamics to two-dimensional electron gas in plane samples and nanotubes located in external magnetic fields we find new kind of wave in electron gas, which is called the spin-electron acoustic wave. Separate spin-up electrons and spin-down electrons evolution reveals in replacement of the Langmuir wave by the couple of hybrid waves. One of two hybrid waves is the modified Langmuir wave. Another hybrid wave is the spin-electron acoustic wave. We study dispersion of these waves in two dimensional structures of electrons. We also consider dependence of dispersion properties on spin polarisation of electrons in external magnetic field.Comment: 5 pages, 5 figure

Observation of Nonspreading Wave Packets in an Imaginary Potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.Comment: 4 figure

Dynamics of the collective modes of an inhomogeneous spin ensemble in a cavity

We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number pass without dispersion from negative to positive valued wave numbers without populating the zero wave number spin wave mode. The results are relevant for multi-mode collective quantum memories where qubits are encoded in different spin waves.Comment: Published version. Some small changes and correction

Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201